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Séminaire Lotharingien de Combinatoire, B32a (1994), 3
pp.

# Jacques Désarménien

# Distribution de l'indice majeur réduit sur les
dérangements

**Abstract.**
The number of derangements of *n* objects, denoted by *d*(*n*),
satisfies the recurrence relation : *d*(*n*)=*nd*(*n*-1)+1 or
*nd*(*n*-1)-1, depending on whether *n* is even or odd. We have
proved in a previous paper how a combinatorial model different
from the usual derangement model provided a simple proof of the
forementioned recurrence. This model has been further exploited
and embedded in the context of symmetric functions. It is also
possible to obtain explicit formulas for the *q*-derangements and
also to study the reduction of the mahonian statistics modulo *n*.
In this paper we show how the notion of reduced major index
yields a direct interpretation of the above formula.

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